What is the difference between learning and non-learning agents?
A learning agent is an agent which has a problem generator, a learning element, a critic and a performance element. ProbGen just creates different instances of a problem w.r.t. a domain and a set of parameters in jurisdiction. A learning element is responsible for making efficient choices and performance element chooses actions for the selected choice. It also changes some of the knowledge base. A critic is basically a metric to tell which is a better choice.

Deep learning is a bit complicated than that. Then again, let's simplify. You see, deep learning is a specific arrangement or subsection of neural networks that helps the learning agent learn faster. That's as simply as I could explain it. What we do is that we arrange the layers in a neural network with a purpose and densely pack it to make it more task specific. Obviously, I am leaving out a lot of implementation details but for them, I am afraid, you need to look up a tutorial.

How are they used in AI?
That's problem specific. Learning agents are everywhere from spam detection to roombas to artificial dog pets. Deep learning on the other hand is currently focused on user pattern recognition and personalization in every front. Please let me know if you need me to expand upon this answer.